Group Theoretical Preliminaries. History of Computational Group Theory (CGT) and Its Place Within Computational Algebra. Methods of Representing Groups on a Computer. Base and Strong Generating Set Methods in Finite Permutation and Matrix Groups. Coset Enumeration. Computation in Finite Nilpotent and Solvable Groups. Representation Theory, Character Theory, and Cohomology. Algorithms Based on the Normal Structure of Finite Groups. Libraries and Databases of Groups. The Matrix Group Recognition Project. Special Techniques for Computing with Very Large Groups and Their Representations. Quotient Algorithms for Finitely Presented Groups. Rewriting Systems and the Knuth-Bendix Completion Process. Automatic Groups (Methods Involving Finite State Automata)